Mu0Poly.h

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/**
 *  @file Mu0Poly.h
 *  Header for a single-species standard state object derived
 *  from \link Cantera::SpeciesThermoInterpType SpeciesThermoInterpType\endlink  based
 *  on a piecewise constant mu0 interpolation
 *  (see \ref spthermo and class \link Cantera::Mu0Poly Mu0Poly\endlink).
 */

// This file is part of Cantera. See License.txt in the top-level directory or
// at http://www.cantera.org/license.txt for license and copyright information.

#ifndef CT_MU0POLY_H
#define CT_MU0POLY_H

#include "cantera/thermo/SpeciesThermoInterpType.h"

namespace Cantera
{
class XML_Node;

//! The Mu0Poly class implements an interpolation of the Gibbs free energy based
//! on a piecewise constant heat capacity approximation.
/*!
 * The Mu0Poly class implements a piecewise constant heat capacity
 * approximation. of the standard state chemical potential of one species at a
 * single reference pressure. The chemical potential is input as a series of
 * (\f$T\f$, \f$ \mu^o(T)\f$) values. The first temperature is assumed to be
 * equal to 298.15 K; however, this may be relaxed in the future. This
 * information, and an assumption of a constant heat capacity within each
 * interval is enough to calculate all thermodynamic functions.
 *
 * The piece-wise constant heat capacity is calculated from the change in the
 * chemical potential over each interval. Once the heat capacity is known, the
 * other thermodynamic functions may be determined. The basic equation for going
 * from temperature point 1 to temperature point 2 are as follows for \f$ T \f$,
 * \f$ T_1 <= T <= T_2 \f$
 *
 * \f[
 *      \mu^o(T_1) = h^o(T_1) - T_1 * s^o(T_1)
 * \f]
 * \f[
 *      \mu^o(T_2) - \mu^o(T_1) = Cp^o(T_1)(T_2 - T_1) - Cp^o(T_1)(T_2)ln(\frac{T_2}{T_1}) - s^o(T_1)(T_2 - T_1)
 * \f]
 * \f[
 *      s^o(T_2) = s^o(T_1) + Cp^o(T_1)ln(\frac{T_2}{T_1})
 * \f]
 * \f[
 *      h^o(T_2) = h^o(T_1) + Cp^o(T_1)(T_2 - T_1)
 * \f]
 *
 *  Within each interval the following relations are used. For \f$ T \f$, \f$
 *  T_1 <= T <= T_2 \f$
 *
 * \f[
 *      \mu^o(T) = \mu^o(T_1) + Cp^o(T_1)(T - T_1) - Cp^o(T_1)(T_2)ln(\frac{T}{T_1}) - s^o(T_1)(T - T_1)
 * \f]
 * \f[
 *      s^o(T) = s^o(T_1) + Cp^o(T_1)ln(\frac{T}{T_1})
 * \f]
 * \f[
 *      h^o(T) = h^o(T_1) + Cp^o(T_1)(T - T_1)
 * \f]
 *
 * Notes about temperature interpolation for \f$ T < T_1 \f$ and \f$ T >
 * T_{npoints} \f$: These are achieved by assuming a constant heat capacity
 * equal to the value in the closest temperature interval. No error is thrown.
 *
 * @note In the future, a better assumption about the heat capacity may be
 *       employed, so that it can be continuous.
 *
 * @ingroup spthermo
 */
class Mu0Poly: public SpeciesThermoInterpType
{
public:
    //! Normal constructor
    /*!
     * In the constructor, we calculate and store the piecewise linear
     * approximation to the thermodynamic functions.
     *
     * @param tlow    Minimum temperature
     * @param thigh   Maximum temperature
     * @param pref    reference pressure (Pa).
     * @param coeffs  Vector of coefficients used to set the parameters for the
     *                standard state for species n. There are \f$ 2+npoints*2
     *                \f$ coefficients, where \f$ npoints \f$ are the number of
     *                temperature points. Their identity is further broken down:
     *            - coeffs[0] = number of points (integer)
     *            - coeffs[1] = \f$ h^o(298.15 K) \f$ (J/kmol)
     *            - coeffs[2] = \f$ T_1 \f$  (Kelvin)
     *            - coeffs[3] = \f$ \mu^o(T_1) \f$ (J/kmol)
     *            - coeffs[4] = \f$ T_2 \f$  (Kelvin)
     *            - coeffs[5] = \f$ \mu^o(T_2) \f$ (J/kmol)
     *            - coeffs[6] = \f$ T_3 \f$  (Kelvin)
     *            - coeffs[7] = \f$ \mu^o(T_3) \f$ (J/kmol)
     *            - ........
     *            .
     */
    Mu0Poly(double tlow, double thigh, double pref, const double* coeffs);

    virtual int reportType() const {
        return MU0_INTERP;
    }

    /*!
     * @copydoc SpeciesThermoInterpType::updateProperties
     *
     * Temperature Polynomial:
     *     tt[0] = temp (Kelvin)
     */
    virtual void updateProperties(const doublereal* tt,
                                  doublereal* cp_R, doublereal* h_RT,
                                  doublereal* s_R) const;

    virtual void updatePropertiesTemp(const doublereal temp,
                                      doublereal* cp_R,
                                      doublereal* h_RT,
                                      doublereal* s_R) const;
    virtual void reportParameters(size_t& n, int& type,
                                  doublereal& tlow, doublereal& thigh,
                                  doublereal& pref,
                                  doublereal* const coeffs) const;

protected:
    //! Number of intervals in the interpolating linear approximation. Number
    //! of points is one more than the number of intervals.
    size_t m_numIntervals;

    //! Value of the enthalpy at T = 298.15. This value is tied to the Heat of
    //! formation of the species at 298.15.
    doublereal m_H298;

    //! Points at which the standard state chemical potential are given.
    vector_fp m_t0_int;

    //! Mu0's are primary input data. They aren't strictly needed, but are kept
    //! here for convenience.
    vector_fp m_mu0_R_int;

    //! Dimensionless Enthalpies at the temperature points
    vector_fp m_h0_R_int;

    //! Entropy at the points
    vector_fp m_s0_R_int;

    //! Heat capacity at the points
    vector_fp m_cp0_R_int;

private:
    //! process the coefficients
    /*!
     * In the constructor, we calculate and store the piecewise linear
     * approximation to the thermodynamic functions.
     *
     * @param coeffs coefficients. These are defined as follows:
     *   - coeffs[0] = number of points (integer)
     *   - coeffs[1] = \f$ h^o(298.15 K) \f$ (J/kmol)
     *   - coeffs[2] = \f$ T_1 \f$  (Kelvin)
     *   - coeffs[3] = \f$ \mu^o(T_1) \f$ (J/kmol)
     *   - coeffs[4] = \f$ T_2 \f$  (Kelvin)
     *   - coeffs[5] = \f$ \mu^o(T_2) \f$ (J/kmol)
     *   - coeffs[6] = \f$ T_3 \f$  (Kelvin)
     *   - coeffs[7] = \f$ \mu^o(T_3) \f$ (J/kmol)
     *   - ........
     */
    void processCoeffs(const doublereal* coeffs);
};

//! Install a Mu0 polynomial thermodynamic reference state
/*!
 * Install a Mu0 polynomial thermodynamic reference state property
 * parameterization for species k into a MultiSpeciesThermo instance, getting
 * the information from an XML database.
 *
 * @param Mu0Node Pointer to the XML element containing the Mu0 information.
 *
 * @ingroup spthermo
 */
Mu0Poly* newMu0ThermoFromXML(const XML_Node& Mu0Node);
}

#endif